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Abstract:

Methods are provided for detecting price manipulation in assets by
receiving data indicating returns on an asset, generating a histogram of
returns data, determining a first area under a curve of the histogram in
a first interval, determining a second area under the curve of the
histogram in a second interval; and calculating a bias ratio which
comprises a ratio based on the first area and the second area.

Claims:

1.-22. (canceled)

23. A system comprising: memory operable to store at least one program;
and at least one processor communicatively coupled to the memory, in
which the at least one program, when executed by the at least one
processor, causes the at least one processor to: receive data indicating
at least two returns of an investment portfolio comprising one or more
assets, said returns being calculated on a periodic basis and indicating
a gain or loss for the investment portfolio for each period; generate a
histogram of the returns data by plotting the returns data on one axis of
the histogram against a standard deviation of the returns data on a
second axis of the histogram; determine a first area under a curve of the
histogram in a first interval comprising a product of a positive standard
deviation of the returns; determine a second area under the curve of the
histogram in a second interval comprising a product of a negative
standard deviation of the returns; calculate a bias ratio wherein a
numerator of the bias ratio comprises the first area and a denominator of
the bias ratio comprises the second area; and analyze the calculated bias
ratio to determine reliability of the returns data wherein the bias ratio
is calculated using the formula: B R = BiasRatio = Count
( r i ) : r i [ 0 , + X σ ] K +
Count ( r i ) : r i [ - X σ , 0 )
, ##EQU00005## where ri is a return, σ represents standard
deviation, X is a positive, non-zero value, K is a positive, non-zero
constant, and ε indicates that ri is within the closed
interval [0,+Xσ] in the case of the numerator and within the half
open interval [-Xσ,0) in the case of the denominator.

24. A system comprising: memory operable to store at least one program;
and at least one processor communicatively coupled to the memory, in
which the at least one program, when executed by the at least one
processor, causes the at least one processor to: receive data indicating
at least two returns of an investment portfolio comprising one or more
assets, said returns being calculated on a periodic basis and indicating
a gain or loss for the investment portfolio for each period; generate a
histogram of the returns data by plotting the returns data on one axis of
the histogram against a standard deviation of the returns data on a
second axis of the histogram; determine a first count of a number of data
in a first interval comprising a product of a positive standard deviation
of the returns; determine a second count of a number of data in a second
interval comprising a product of a negative standard deviation of the
returns; and calculate a bias ratio wherein a numerator of the bias ratio
comprises the first count and a denominator of the bias ratio comprises
the second count; and analyze the calculated bias ratio to determine
reliability of the returns data wherein the bias ratio is calculated
using the formula: B R = BiasRatio = Count ( r i )
: r i [ 0 , + X σ ] K + Count ( r
i ) : r i [ - X σ , 0 ) ,
##EQU00006## where ri is a return, σ represents standard
deviation, X is a positive, non-zero value, K is a positive, non-zero
constant, and ε indicates that ri is within the closed
interval [0,+Xσ] in the case of the numerator and within the half
open interval [-Xσ,0) in the case of the denominator.

25. The system of claim 23 wherein one or more of the one or more assets
in the investment portfolio are valued with reference to subjective
criteria.

26. The system of claim 24 wherein one or more of the one or more assets
in the investment portfolio are valued with reference to subjective
criteria.

27. A system comprising: memory operable to store at least one program;
and at least one processor communicatively coupled to the memory, in
which the at least one program, when executed by the at least one
processor, causes the at least one processor to: receive data indicating
at least two returns of an investment portfolio comprising one or more
assets, said returns being calculated on a periodic basis and indicating
a gain or loss for the investment portfolio for each period; generate a
histogram of the returns data by plotting the returns data on one axis of
the histogram against a standard deviation of the returns data on a
second axis of the histogram; determine a first area under a curve of the
histogram in a first interval comprising a product of a positive standard
deviation of the returns; determine a second area under the curve of the
histogram in a second interval comprising a product of a negative
standard deviation of the returns; calculate a bias ratio wherein a
numerator of the bias ratio comprises the first area and a denominator of
the bias ratio comprises the second area; and analyze the calculated bias
ratio to determine reliability of the returns data wherein the bias ratio
is calculated using the formula: B R = ∫ 0 X
σ r r K + ∫ - X σ 0
r r , ##EQU00007## where r is a function representing a
distribution of returns (dr), σ represents standard deviation, X is
a positive, non-zero value, and K is a positive, non-zero constant.

28. A system comprising: memory operable to store at least one program;
and at least one processor communicatively coupled to the memory, in
which the at least one program, when executed by the at least one
processor, causes the at least one processor to: receive data indicating
at least two returns of an investment portfolio comprising one or more
assets, said returns being calculated on a periodic basis and indicating
a gain or loss for the investment portfolio for each period; generate a
histogram of the returns data by plotting the returns data on one axis of
the histogram against a standard deviation of the returns data on a
second axis of the histogram; determine a first count of a number of data
in a first interval comprising a product of a positive standard deviation
of the returns; determine a second count of a number of data in a second
interval comprising a product of a negative standard deviation of the
returns; and calculate a bias ratio wherein a numerator of the bias ratio
comprises the first count and a denominator of the bias ratio comprises
the second count; and analyze the calculated bias ratio to determine
reliability of the returns data wherein the bias ratio is calculated
using the formula: B R = ∫ 0 X σ r
r K + ∫ - X σ 0 r r
, ##EQU00008## where r is a function representing a distribution of
returns (dr), σ represents standard deviation, X is a positive,
non-zero value, and K is a positive, non-zero constant.

29. The system of claim 27 wherein one or more of the one or more assets
in the investment portfolio are valued with reference to subjective
criteria.

30. The system of claim 28 wherein one or more of the one or more assets
in the investment portfolio are valued with reference to subjective
criteria.

Description:

PRIORITY APPLICATION

[0001] This application claims the benefit of U.S. Provisional Patent
Application No. 60/859,838, filed Nov. 16, 2006, titled Bias Ratio
Measuring the Shape of Fraud. The entire contents of that application are
incorporated herein by reference.

INTRODUCTION

[0002] Before purchasing any type of asset, investors typically conduct an
assessment of the asset. This assessment typically considers certain
statistics of the asset such as purchase price, historic and predicted
returns, periodic growth, periodic dividends, Sharpe ratios, or other
relevant statistics. Some assets, such as illiquid assets, can be
difficult to price reliably. In such cases, prices may be obtained from
various sources, including multiple dealers. Since each dealer can
provide a different price, and the prices may vary widely, it can be
difficult to establish a true price or other statistic for such assets.

[0003] The inventions described herein overcome certain limitations in
existing methods and systems for evaluating pricing of assets.

[0004] In one embodiment of the invention, a method is provided
comprising: receiving data indicating at least two returns of an asset;
generating a histogram of the returns data; determining a first area
under a curve of the histogram in a first interval; determining a second
area under the curve of the histogram in a second interval; and
calculating a bias ratio wherein a numerator comprises at least the first
area and a denominator comprises at least the second area. Variations of
the embodiment include establishing a benchmark to compare with the bias
ratio, flagging the asset if the calculated bias ratio exceeds the
benchmark, the first interval is the first standard deviation of positive
returns and the second interval is the first standard deviation of
negative returns, the returns in the first interval are positive returns
and the returns in the second interval are negative returns. In some
embodiments, the bias ratio is an indicator of reliability of the data
and can be calculated using the formula:

where r is a function representing the distribution of returns and K is a
constant.

[0005] In another embodiment of the invention, a method is provided
comprising: calculating a first area of a first interval of a histogram
of returns data indicating at least two returns of an asset; wherein the
returns in the first interval are positive; calculating a second area of
a second interval of the histogram of the returns data, wherein the
returns in the second interval are negative; and determining a bias ratio
based on the first area and second area. Variations of the embodiment
include that the bias ratio numerator comprises at least the first area
and the bias ratio denominator comprises at least the second area, the
first interval is a first standard deviation of positive returns and the
second interval is a first standard deviation of negative returns.

[0006] In another embodiment of the invention, a method is provided
comprising: receiving data indicating at least two returns of an asset;
obtaining a first count of a number of data in a first interval;
obtaining a second count of a number of data in a second interval; and
calculating a bias ratio wherein a numerator comprises the first count
and a denominator comprises the second count. Variations of the
embodiment include establishing a benchmark to compare with the bias
ratio, flagging the asset if the calculated bias ratio exceeds the
benchmark, the first interval is a first standard deviation of positive
returns and the second interval is a first standard deviation of negative
returns, and the returns in the first interval are positive returns and
the returns in the second interval are negative returns.

[0007] In another embodiment of the invention, a ratio for verifying an
asset return is provided comprising: a first area divided by the sum of a
second area and a small, positive constant, the first area and second
area being areas under a curve of a histogram of asset returns in two
adjacent intervals. Variations of the ratio include that the two adjacent
intervals comprise a first standard deviation of positive returns and a
first standard deviation of negative returns, and the returns in the
first interval are positive returns and the returns in the second
interval are negative returns.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIG. 1 depicts two histograms of monthly returns;

[0009] FIG. 2 depicts a flow diagram of a method according to an
embodiment of the invention;

[0010] FIG. 3 depicts a flow diagram of a method according to another
embodiment of the invention; and

[0011] FIG. 4 depicts a block diagram of a computer system for providing a
method according to an embodiment of the invention.

DETAILED DESCRIPTION

[0012] Embodiments of the invention relate to evaluating asset statistics,
such as an asset price or return. Although not specifically described in
the examples, the invention may be equally applied to any type of
statistics which may be manipulated or for which uncertainties may exist.

[0013] Some investment portfolios may not be reliably priced because
underlying assets may not have a definitive market quote and a source of
price or other asset data may not be transparent. For such assets, price
can be obtained by polling dealers; and the prices received from the
dealers can be used to calculate returns. However, the poll dealer's
prices may vary widely. For example, Table 1 lists the minimum, maximum
and average prices for several quotes obtained on seventeen securities.
As indicated in the last column, the quotes have a range as high as
nearly 70%.

[0014] To price a portfolio, such as one based on the securities listed in
Table 1, standard market practice allows a manager to discard any price
outliers, average the remaining prices of each security, and sum the
values of the priced securities. Outliers are not necessarily strictly
defined and may be subject to a heuristic rule that "you know it when you
see it." Visible outliers may be an indication of the particular
security's characteristics and liquidity as well as the market
environment in which quotes are solicited, or the outlier may simply be a
data error. After discarding outliers, the value of a security may be
obtained by averaging the remaining price quotes. The total value of the
portfolio, which is referred to as Net Asset Value ("NAV") is obtained by
summing the individual security values.

[0015] NAV is typically calculated at the end of every business day. The
change in NAV at the end of a period, such as a month, after adjustment
for capital flows into and out of the fund, determines whether the fund
has had a gain or loss for that period. This determination is critical to
the success of the fund. It is also a determination that can be
manipulated. Consider, for example, one NAV calculation obtained after
discarding no outliers (or only some outliers) that results in a small
loss for the period, e.g., -0.01%. A review of the quotes used to obtain
this NAV may show that the pricing calculation included a dealer quote
that was 50% below all the other prices for a particular security.
Removing that single quote as an outlier could raise the return for that
period to +0.01%. In this scenario, an investment manager can either use
the first calculation (Option 1, in which the outlier was not discarded)
resulting in a loss or use the second calculation (Option 2, in which the
outlier was discarded) showing a gain, and optionally document a reason
for discarding the outlier.

[0016] FIG. 1 depicts two histograms 10 and 20 based on calculations using
Options 1 (10) and 2 (20). Both histograms plot the number of months that
the return on a portfolio fell within one or more standard deviations
(σ) above or below zero. As is well known, the standard deviation
is the root mean square (RMS) deviation of values, in this case, the
returns, from their arithmetic mean. The smooth histogram 10 plots the
distribution of returns calculated using Option 1, and the kinked
histogram 20 plots the distribution of returns calculated using Option 2.
Since typical investment managers wish to present a fund that has
consistent positive returns, return distributions are often generated
along the lines of histogram 20. Calculations using Option 2 typically
produce more small positive results and fewer small negative returns than
calculations that use Option 1.

[0017] As shown in FIG. 1, significant inconsistencies between the plots
of histograms 10 and 20 are manifested in the hump at the -1.5 Standard
Deviation point and in a gap between the two plots in the interval
-1σ to 0.0. Although calculations using Option 2 compared to Option
1 may not individually, or collectively, misrepresent return volatility,
recent financial history has shown that hiding small losses (by
discarding certain outliers) can eventually lead to large losses, e.g.,
the Sumitomo copper affair as well as the demise of Barings.

[0018] The area in the returns histograms of FIG. 1 between the two lines
of histograms 10 and 20 represents the difference in calculations
generated with price manipulations. One way to determine whether price
manipulations have occurred is to model or approximate the area between
the two lines. Since this area, in particular, in the interval of the
histogram between -1.0σ and zero can be difficult to model
precisely, behavior induced modifications may be manifested in a shape of
the returns histogram in the intervals around zero.

[0019] In accordance with one embodiment of the invention, one test for
detecting price manipulation manifested in a returns histogram is a
counting test. A flow chart depicting one such test is set forth in FIG.
2. As shown in FIG. 2, returns data are received at step 210, and are
processed at step 220 to obtain a mean and a standard deviation. Next, at
step 230, the number of times the return falls within one standard
deviation above zero and the number of times the return falls within one
standard deviation below zero are counted. For example, a first count is
obtained for all results in the interval from zero to +1σ, as well
as a second count for all results in the interval from zero to -1σ.
A Bias Ratio is then obtained at step 240 by forming a quotient from the
first and second counts.

[0020] The Bias Ratio is used as an indicator of price manipulation.
Typically, higher Bias Ratios indicate that manipulation is likely to
have occurred. Therefore, a Bias Ratio threshold may be established
against which the calculated Bias Ratio is compared at step 250. When the
Bias Ratio exceeds the threshold, the returns data is flagged as likely
to have been manipulated.

where K is a small, positive, non-zero, constant used to avoid the
possibility of dividing by zero.

[0026] While intervals in the above example are standard deviations from
[-1.0σ to 0) and [0 to +1.0σ], other intervals may be used as
will be understood by one of skill in the art. In general, the intervals
of interest are the adjacent intervals on either side of a critical value
in the distribution.

[0027] The Bias Ratio approximates a ratio between an area under the
returns histogram immediately above zero and the similar or corresponding
area immediately below zero. The Bias Ratio typically holds the following
properties:

[0028] a. 0≦BR≦n

[0029] b. If ri≦0,
.A-inverted. i, then BR=0

[0030] c. If .A-inverted. ri such that
ri>0, ri>1.0σ then BR=0

[0031] d. If the
distribution ri is Normal with mean=0, the BR→1.0 as
n→∞.

[0032] In a second embodiment, shown in the flowchart of FIG. 3, the Bias
Ratio is calculated by obtaining an area in two intervals of a returns
histogram. As shown in FIG. 3, returns data is received at step 310, and
is processed at step 320 to obtain a mean and a standard deviation. The
returns data is used to generate a histogram and a distribution function
r is fitted to the histogram data. The area under the distribution
function is calculated at step 330 for two intervals, one immediately
above zero and the other immediately below zero. The Bias Ratio is
determined at step 340 according to the formula:

B R = ∫ 0 1.0 σ r r K +
∫ - 1.0 σ 0 r r , ##EQU00004##

where K is a small, positive, non-zero, constant used to avoid the
possibility of dividing by zero.

[0033] As described previously, the Bias Ratio can be used as an
indication of price manipulation. Thus, at step 350, the calculated Bias
Ratio is compared with a threshold Bias Ratio and the fund returns are
flagged if the Bias Ratio exceeds the threshold.

[0034] The Bias Ratio defined by a la interval around zero can work well
to discriminate pricing, returns and other statistics among hedge funds.
Other intervals may be used to provide metrics with varying resolutions.

[0035] Inventions described herein may be automated and used in the
exemplary system of FIG. 4. As shown, client computers 400 communicate
via network 410 with a central server 430 which is coupled to one or more
databases 440, one or more processors 450, and software 460. Other
components and combinations of components may also be used to support
Bias Ratio or other calculations described herein as will be evident to
one of skill in the art. Server 430 facilitates communication of returns
data from a database 440 to and from clients 400. Processor 450 provides
calculations relevant to calculating a Bias Ratio, or other financial
calculations. Software 460 can be installed locally at a client 400
and/or centrally supported for facilitating Bias Ratio calculations and
applications. For example, software 460 may be used in embodiments where
a threshold for a Bias Ratio is established.

[0036] Examples of Bias Ratio calculations for indices are presented in
Table 2. Table 2 includes data relating to numerous indices, including an
annualized average return, an associated Sharpe ratio, a Standard
Deviation and Bias Ratio. Calculations included in Table 2 are based on
monthly data over a time period greater than 9 years with the exception
of the Hennessee H.F. High Yield index which includes data spanning 7.5
years.

[0037] Generally, assets with a high Sharpe ratio are considered to
provide greater return per risk. When compared to the Bias Ratio results
of Table 2, there is a correlation between a high Sharpe ratio and an
increasing Bias Ratio.

[0038] Bias Ratios of market and hedge fund indices give some insight into
a natural shape of returns near zero. Theoretically, demand for markets
with normally distributed returns around a zero mean may not be expected.
Such markets typically have distributions with a Bias Ratio of less than
1.0. Major market indices support this trend and have Bias Ratios
generally greater than 1.0 over long time periods. The returns of equity
and fixed income markets as well as alpha generating strategies have a
natural positive skew of returns which provide a smoothed histogram as a
positive slope near zero. Fixed income strategies with a relatively
constant positive return ("carry") also exhibit total return series with
a naturally positive slope near zero. Cash investments such as 90-day
T-Bills have large Bias Ratios (i.e., that risk is relatively low), since
they generally do not experience periodic negative returns. Consequently,
the Bias Ratio is less reliable for hedge funds that have an unleveraged
portfolio with a high cash balance.

[0039] Bias Ratios vs. Sharpe ratios

[0040] The Sharpe ratio measures risk-adjusted returns, and valuation
biases are expected to understate volatility. An unexpectedly high Sharpe
ratio may be a flag for skeptical practitioners to detect smoothing.
(Weisman, Andrew, "Dangerous Attractions: Informationless Investing and
Hedge Fund Performance Measurement Bias", 2002, Journal of Portfolio
Management.) Data may not support a strong statistical relationship
between a high Bias Ratio and a high Sharpe ratio. High Bias Ratios exist
in strategies that have traditionally exhibited high Sharpe ratios, but
many assets have high Bias Ratios and low Sharpe ratios.

[0041] The Bias Ratio and Serial Correlation

[0042] Hedge fund investors can use serial correlation (autocorrelation)
to detect smoothing in hedge fund returns. Market frictions such as
transaction costs and information processing costs that cannot be
arbitraged may lead to serial correlation. Stale prices for illiquid
assets may have the same effect. Managed prices can also be a cause for
serial correlation. As mentioned previously, fund managers of illiquid,
hard to price assets, may use some leeway to calculate a fund's NAV. When
returns are smoothed by marking securities conservatively in the good
months and aggressively in the bad months a manager may add a serial
correlation as a side effect. The more liquid a fund's securities, the
less leeway the manager has to make up numbers. (Lo, Andrew W.; "Risk
Management For Hedge Funds: Introduction and Overview", White Paper,
June, 2001.)

[0044] Serial correlations appear in many cases that are likely not the
result of willful manipulation but rather the result of stale prices and
illiquid assets. Both Sun Asia and Plank (fictitious names are used to
represent real hedge funds) are emerging market hedge funds with NAVs
based on objective prices. However, both funds show significant serial
correlation. The presence of serial correlation in several market indices
such as the JASDAQ and the SENSEX indicates that serial correlation might
not be suitable for uncovering price manipulation. However two known
problematic funds, namely Bayou, an Equity fund, and Safe Harbor, an MBS
fund have relatively high calculated Bias Ratios which stand out from
Bias Ratios of other funds. In contrast, Sharpe ratios and PVQ6 for the
Bayou fund and Safe Harbor fund do not stand out in comparison with the
other funds. Thus, the Bias Ratio provides price manipulation indication
which other known risk indicators miss.

[0045] Benchmark Bias Ratios by Hedge Fund Strategies

[0046] Some hedge fund strategy indices may not generate benchmark Bias
Ratios because aggregated monthly returns can mask individual manager
behavior, e.g., pricing decisions. However, Bias Ratios can be calculated
at the manager level and then aggregated to create useful benchmarks.

[0047] Variability of Bias Ratios for Different Strategies

[0048] Funds that employ illiquid assets can have Bias Ratios that are
significantly higher than the Bias Ratios of indices representing the
underlying asset class. For example, most equity indices have Bias Ratios
falling between 1.0 and 1.5. In one sample of funds, equity hedge funds
had Bias Ratios ranging from 0.3 to 3.0 with an average of 1.29 and
standard deviation of 0.5. On the other hand, the Lehman Aggregate MBS
Index has a Bias Ratio of 2.16, while MBS hedge funds in the sample have
Bias Ratios from 1.7 to 31.0, with an average of 7.7 and standard
deviation of 7.5. Ceteris paribus, a high Bias Ratio for an equity based
strategy might be unremarkable for an MBS strategy. Calculations for such
funds are shown in Table 4:

[0050] Investors ideally examine prices of each individual underlying
asset that comprises a manager's portfolio, or other priced assets.
However, in the case of limited price transparency, and time and effort,
investors may not have access to price or other statistical information.
The Bias Ratio provides an efficient method to highlight pricing
problems. The Bias Ratio can be used to differentiate among a universe of
funds and assets. If a fund has a Bias Ratio above a certain benchmark,
median level or other threshold, closer inspection of the assets, pricing
policy, and other supporting information may be warranted; whereas, well
below the median might warrant only a cursory inspection.

[0051] The Bias Ratio can also be useful to detect illiquid assets
forensically. For example, if a database search for Long/Short Equity
managers reveals a fund with a reasonable history and a Bias Ratio
greater than 2.5, detailed diligence will likely reveal some fixed income
or highly illiquid equity investments in the portfolio.

[0052] The Bias Ratio can provide an indication of a) illiquid assets in a
portfolio combined with b) a subjective pricing policy. Most
valuation-related hedge fund debacles have exhibited high Bias Ratios.
However, the converse may not always be true.

[0053] It will be appreciated that the present invention has been
described by way of example only, and that the invention is not to be
limited by the specific embodiments described herein. Improvements and
modifications may be made to the invention without departing from the
scope or spirit thereof.

[0054] Embodiments of the present invention comprise computer components
and computer-implemented steps that will be apparent to those skilled in
the art. For example, calculations and communications can be performed
electronically, and agreements can be composed, transmitted and executed
electronically.

[0055] For ease of exposition, not every step or element of the present
invention is described herein as part of a computer system, but those
skilled in the art will recognize that each step or element may have a
corresponding computer system or software component. Such computer system
and/or software components are therefore enabled by describing their
corresponding steps or elements (that is, their functionality), and are
within the scope of the present invention.